My research interests are in developing upscaled models, dimensional reduction and numerical algorithms for  coupled multiphysics processes such as flow and transport in deformable porous media. The reactive flow models lead to changes in the geometry at the pore scale and require non-standard models for describing the processes. I have performed upscaling and dimensional reduction of such reactive processes and developed numerical methods for  solving the upscaled models. I have also worked on scalable algorithms such as domain decomposition techniques for simulating multiphase flow and transport in porous media. In addition, I have worked on the analysis of  iterative and multirate algorithms for solving the  coupled flow and geomechanics problems in a  porous medium.

 

I have finished two courses in Pedagogy from Karlstad University, Sweden. These two courses are Teaching in Higher Education I and Supervising Doctoral and Licentiate Students. This corresponds to a total of 10 full weeks of training, that is, 400 hours of training (15 ECTS).

University of Bergen, Department of Mathematics

Responsible lecturer for Continuum Mechanics, Spring 2020, Spring 2021, Spring 2022, Spring 2023

Responsible lecturer for Numerical Linear Algebra, Fall 2020, Fall 2021

Responsible lecturer for Computational Science II, Spring 2015, Spring 2016, Spring 2017, Spring 2018

Responsible lecturer for Finite Element Analysis, Fall 2015, Fall 2017, Fall 2022

Responsible lecturer for Vector and Tensor Analysis, Fall 2016

Co-responsible (Main responsible: Prof. Helge Dahle) for Ordinary Differential Equations, Spring 2023

Karlstad University Sweden, Department of Mathematics and Computer Science

Responsible lecturer for Ordinary Differential Equations, Fall 2018,

Responsible lecturer for Advanced Linear Algebra, Spring 2019,

Responsible lecturer for Complex Analysis and Transforms, Spring 2019

Optimization, Spring 2019

Teaching at Eindhoven University of Technology, The Netherlands

Instructor, Advanced Calculus 2008-09, 2009-10, 2010-11.

Instructor, Vector Calculus 2009-2010.

 

Academic book chapter

• Jakob Seierstad Stokke; Morten Jakobsen; Kundan Kumar et al. (2025). A History-Dependent Dynamic Biot Model. (external link)
• Vinod Laguri; Kundan Kumar; Pradeep Gupta et al. (2023). Thermodynamic analysis of a multi-evaporator refrigeration cycle using a two-phase ejector as an expansion device. (external link)
• David Landa-Marbán; Kundan Kumar; Sarah Eileen Gasda et al. (2021). Numerical studies of long-term wettability alteration effects in CO2 storage applications. (external link)
• David Landa-Marbán; Kundan Kumar; Svenn Tveit et al. (2021). Numerical studies of CO2 leakage remediation by MICP-based plugging technology. (external link)
• Jakub Both; Kundan Kumar; Jan Martin Nordbotten et al. (2017). Iterative Methods for Coupled Flow and Geomechanics in Unsaturated Porous Media. (external link)
• Kundan Kumar; R.M. Chandima Ratnayake (2017). Maintenance Regime Minimum (MRM): State of the Art — Maintaining Offshore Platforms Before Decommissioning. (external link)
• Abay Kassa; Sarah Gasda; Kundan Kumar et al. (2018). Impact of Wettability Evolution on Dynamic Capillary Pressure. (external link)

Conference lecture

• Kundan Kumar (2021). Upscaling of flow models in a fractured media. (external link)
• Sarah Eileen Gasda; Abay Kassa; Florin Adrian Radu et al. (2018). A Model for Dynamic Capillary Pressure with Time-Dependent Wettability Alteration. (external link)
• Abay Kassa; Sarah Gasda; Kundan Kumar et al. (2018). Impact of Wettability Evolution on Dynamic Capillary Pressure. (external link)
• Sarah Eileen Gasda; David Landa-Marbán; Abay Kassa et al. (2022). Modeling and Simulation of Long-term Wettability Alteration on CO2 Storage Efficiency and Containment. (external link)
• Sarah Eileen Gasda; David Landa-Marbán; Abay Kassa et al. (2022). Modeling and Simulation of Wettability Alteration for CO2 Storage. (external link)
• Kundan Kumar; Ingeborg Gåseby Gjerde; Jan Martin Nordbotten et al. (2017). Solution strategies for the coupling of mixed dimensional problems. (external link)
• Kundan Kumar (2021). Monotonicity of Effective Tensors with Respect to Geometric Perturbations. (external link)
• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten (2019). Analysis and approximation of coupled 1D-3D flow models. (external link)
• Jakub Wiktor Both; Kundan Kumar; Jan Martin Nordbotten et al. (2021). Robust block-partitioned solvers for flow in deformable porous media via alternating minimization. (external link)
• Ingeborg Gåseby Gjerde; Kundan Kumar (2017). Mixed methods for hierarchical flow models for wells in porous media. (external link)
• David Landa-Marbán; Kundan Kumar; Svenn Tveit et al. (2021). Numerical studies of CO2 leakage remediation by MICP-based plugging technology. (external link)
• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten (2019). The mathematical structure of coupled 1D-3D flow models. (external link)
• David Landa-Marbán; Kundan Kumar; Sarah Eileen Gasda et al. (2021). Numerical studies of long-term wettability alteration effects in CO2 storage applications. (external link)
• Abay Kassa; Sarah Eileen Gasda; Florin Adrian Radu et al. (2018). Impact of Time-Dependent Wettability Alteration on Capillary Pressure. (external link)
• Jakub Wiktor Both; Kundan Kumar; Jan Martin Nordbotten et al. (2021). Robust block-partitioned solvers for poroelasticity derived from its gradient flow structures. (external link)
• Jakub Wiktor Both; Kundan Kumar; Jan Martin Nordbotten et al. (2021). Block-partitioned solvers for poromechanics via gradient flows and minimization. (external link)
• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten (2018). Well Modelling By Means Of Coupled 1D-3D Flow Models . (external link)
• David Landa-Marbán; Svenn Tveit; Sarah Eileen Gasda et al. (2022). py-micp: An Open-Source Simulation Workflow for Field-Scale Application of Microbially Induced Calcite Precipitation Technology for Leakage Remediation. (external link)
• David Landa-Marbán; Svenn Tveit; Kundan Kumar et al. (2021). Numerical studies of microbially induced calcite precipitation at the field scale. (external link)
• Kundan Kumar (2021). Using MRST for Solving Multiphase Flow Models in Porous Media. (external link)
• Kundan Kumar (2021). Homogenization of Reactive Flows in Porous Media. (external link)
• David Landa-Marbán; Na Liu; Iuliu Sorin Pop et al. (2019). Mathematical modelling of the bio-plug technology: laboratory experiments, upscaling, and numerical simulations. (external link)
• Ingeborg Gåseby Gjerde; Kundan Kumar (2017). Mixed methods for hierarchical flow models for wells in porous media. (external link)
• David Landa-Marbán; Svenn Tveit; Kundan Kumar et al. (2021). ad-micp: A third-party module for MRST to study CO2 leakage remediation by microbially induced calcite precipitation. (external link)
• Jakub Both; Kundan Kumar; Jan Martin Nordbotten et al. (2020). Robust Block-Partitioned Solvers for Poroviscoelasticity. (external link)
• Kundan Kumar; Ingeborg Gåseby Gjerde; Jan Martin Nordbotten et al. (2017). Solution strategies for a 3D-1D coupling model. (external link)
• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten (2019). Coupled 1D-3D flow models. (external link)
• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten (2018). The Mathematical Structure of Coupled 1D-3D Models. (external link)
• Abay Kassa; Sarah Gasda; Kundan Kumar et al. (2019). Constitutive relations modelling for dynamically altered porous medium. (external link)
• David Landa-Marbán; Adrian Florin Radu; Iuliu Sorin Pop et al. (2017). An upscaled model for permeable biofilm formation in a thin strip. (external link)
• Kundan Kumar (2017). Coupled Problems in Porous Media. (external link)
• David Landa-Marbán; Svenn Tveit; Kundan Kumar et al. (2020). Modeling and Simulations of Microbially Induced Calcite Precipitation. (external link)
• David Landa-Marbán; Gunhild Bødtker; Bartek Florczyk Vik et al. (2020). Numerical simulations of biofilms in core samples: MEOR and MICP. (external link)

Conference poster

• David Landa-Marbán; Na Liu; Iuliu Sorin Pop et al. (2018). Mathematical modeling of biofilm formation: from the pore-scale to the core-scale. (external link)
• David Landa-Marbán; Na Liu; Iuliu Sorin Pop et al. (2019). Biofilms in porous media: laboratory experiments, mathematical modeling and upscaling. (external link)
• David Landa-Marbán; Na Liu; Sorin Iuliu Pop et al. (2018). Mathematical modelling of bacterial growth at different scales: numerical simulations and laboratory experiments. (external link)
• Hasan Gürsel; Geir Ersland; Sarah Eileen Gasda et al. (2025). Modeling the Temporal Dynamics of Formation Damage during Produced Water Re-injection. (external link)
• Abay Kassa; Sarah Gasda; Kundan Kumar et al. (2019). Constitutive relations for dynamic wettability transition zones. (external link)
• David Landa-Marbán; Na Liu; Iuliu Sorin Pop et al. (2017). A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments. (external link)
• Hasan Gürsel; Geir Ersland; Sarah Eileen Gasda et al. (2024). Modeling the Temporal Dynamics of Formation Damage during Produced Water Re-injection. (external link)
• Geir Ersland; Sarah Eileen Gasda; Kundan Kumar (2024). Modeling the Temporal Dynamics of Formation Damage during Produced Water Re-injection. (external link)
• Hasan Gürsel; Geir Ersland; Sarah Eileen Gasda et al. (2024). Modeling the Temporal Dynamics of Formation Damage during Produced Water Re-injection. (external link)

Master’s thesis

• Florin Adrian Radu; Kassa Abay; Kundan Kumar (2016). Mathematical Modeling of Optimal Control Strategy for Microbial Enhanced Oil Recovery Processes. (external link)
• Florin Adrian Radu; Mofrad Abolpour Samaneh; Kundan Kumar (2016). Microbially enhanced techniques for oil recovery and clogging.. (external link)

Academic article

• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten et al. (2019). Splitting method for elliptic equations with line sources. (external link)
• Manuel Antonio Borregales Reveron; Kundan Kumar; Florin Adrian Radu et al. (2018). A partially parallel-in-time fixed-stress splitting method for Biot’s consolidation model. (external link)
• David Landa-Marbán; Svenn Tveit; Kundan Kumar et al. (2021). Practical approaches to study microbially induced calcite precipitation at the field scale. (external link)
• Leonid Vasilyev; Jan Martin Nordbotten; Florin Adrian Radu et al. (2017). On the Properties of the Parameter Space of the Generalized Continuum Transport Model for Description of Fluid Flow in Porous Networks. (external link)
• Carina Bringedal; Kundan Kumar (2017). Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow. (external link)
• Adrian Florin Radu; Iuliu Sorin Pop; Florian List et al. (2020). Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. (external link)
• Jakub Both; Kundan Kumar; Jan Martin Nordbotten et al. (2019). Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations. (external link)
• Abay Kassa; Kundan Kumar; Sarah Gasda et al. (2020). Implicit linearization scheme for nonstandard two-phase flow in porous media. (external link)
• Ruichao Ye; Kundan Kumar; Maarten V. de Hoop et al. (2020). A multi-rate iterative coupling scheme for simulating dynamic ruptures and seismic waves generation in the prestressed earth. (external link)
• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten (2019). A singularity removal method for coupled 1D–3D flow models. (external link)
• David Landa-Marban; Na Liu; Iuliu Sorin Pop et al. (2018). A pore-scale model for permeable biofilm: Numerical simulations and laboratory experiments. (external link)
• Florin Adrian Radu; Kundan Kumar; Jan Martin Nordbotten et al. (2017). A robust, mass conservative scheme for two-phase flow in porous media including Hoelder continuous nonlinearities. (external link)
• Abay Kassa; Sarah Eileen Gasda; David Landa-Marbán et al. (2022). Field-scale impacts of long-term wettability alteration in geological CO2 storage. (external link)
• Manuel Antonio Borregales Reveron; Kundan Kumar; Jan Martin Nordbotten et al. (2020). Iterative solvers for Biot model under small and large deformations. (external link)
• Tameem Almani; Kundan Kumar; Ali H. Dogru et al. (2016). Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. (external link)
• Tameem Almani; AM Manea; Kundan Kumar et al. (2019). Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. (external link)
• Erlend Storvik; Jakub Both; Kundan Kumar et al. (2019). On the optimization of the fixed‐stress splitting for Biot's equations. (external link)
• Kundan Kumar; Svetlana Kyas; Jan Martin Nordbotten et al. (2020). Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem. (external link)
• Jakub Both; Manuel Antonio Borregales Reveron; Kundan Kumar et al. (2017). Robust fixed stress splitting for Biot's equations in heterogeneous media. (external link)
• Tameem Almani; Kundan Kumar; Mary F. Wheeler (2023). Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media. (external link)
• David Landa-Marbán; Iuliu Sorin Pop; Kundan Kumar et al. (2019). Numerical Simulation of Biofilm Formation in a Microchannel. (external link)
• Martin Sandanger Dugstad; Kundan Kumar; Øystein Pettersen (2021). Dimensional reduction of a fractured medium for a polymer EOR model. (external link)
• T. Almani; Kundan Kumar (2022). Convergence of single rate and multirate undrained split iterative schemes for a fractured biot model. (external link)
• Abay Kassa; Sarah Gasda; Kundan Kumar et al. (2020). Impact of time-dependent wettability alteration on the dynamics of capillary pressure. (external link)
• Neda Sepasian; Kundan Kumar; Marcel Breeuwer (2015). A geometrical approach to find corresponding patches in 3D medical surfaces. (external link)
• David Landa Marban; Gunhild Bødtker; Kundan Kumar et al. (2020). An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube. (external link)
• T. Almani; Kundan Kumar (2024). Convergence of multirate fixed stress split iterative schemes for a fractured Biot model. (external link)
• Kundan Kumar; Tameem Almani; Gurpreet Singh et al. (2016). Multirate undrained splitting for coupled flow and geomechanics in porous media. (external link)
• Iuliu Sorin Pop; Jeroen Bogers; Kundan Kumar (2017). Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition. (external link)
• Vivette Girault; Kundan Kumar; Mary Fanett Wheeler (2016). Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium. (external link)
• Kundan Kumar; Maria Neuss-Radu; Iuliu Sorin Pop (2016). Homogenization of a pore scale model for precipitation and dissolution in porous media. (external link)
• Florian List; Kundan Kumar; Iuliu Sorin Pop et al. (2020). Rigorous upscaling of unsaturated flow in fractured porous media. (external link)
• David Landa Marban; Gunhild Bødtker; Bartek Florczyk Vik et al. (2020). Mathematical modeling, laboratory experiments, and sensitivity analysis of bioplug technology at Darcy scale. (external link)
• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten (2021). A Mixed Approach to the Poisson Problem with Line Sources. (external link)
• Manuel Antonio Borregales Reveron; Florin Adrian Radu; Kundan Kumar et al. (2018). Robust iterative schemes for non-linear poromechanics. (external link)
• Shridhar Kumar; Pratibhamoy Das; Kundan Kumar (2024). Adaptive mesh based efficient approximations for Darcy scale precipitation–dissolution models in porous media. (external link)
• Tameem Almani; Kundan Kumar; M.F Wheeler (2017). Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. (external link)
• Adrian Florin Radu; Jan Martin Nordbotten; Iuliu Sorin Pop et al. (2015). A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media. (external link)
• Nadia Skoglund Taki; Kundan Kumar (2024). Well-posedness of evolutionary differential variational–hemivariational inequalities and applications to frictional contact mechanics. (external link)
• T Almani; Kundan Kumar; G. Singh et al. (2019). Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium. (external link)
• Maarten V. de Hoop; Kundan Kumar; Ruichao Ye (2020). Analysis of dynamic ruptures generating seismic waves in a self-gravitating planet: An iterative coupling scheme and well-posedness. (external link)
• Jakub Both; Kundan Kumar; Jan Martin Nordbotten et al. (2018). Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. (external link)
• Johannes Kraus; Kundan Kumar; Maria Lymbery et al. (2024). A fixed-stress splitting method for nonlinear poroelasticity. (external link)
• Abay Kassa; Sarah E. Gasda; Kundan Kumar et al. (2021). Modeling of relative permeabilities including dynamic wettability transition zones. (external link)
• Kundan Kumar; Florian List; Iuliu Sorin Pop et al. (2020). Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. (external link)
• Martin Sandanger Dugstad; Kundan Kumar (2022). Dimensional reduction of a fractured medium for a two-phase flow. (external link)
• Max Akira Endo Kokubun; Florin Adrian Radu; Eirik Keilegavlen et al. (2018). Transport of polymer particles in oil–water flow in porous media: Enhancing oil recovery. (external link)

Conference abstract

• Abay Kassa; Sarah Gasda; Kundan Kumar et al. (2018). Impact of time-dependent wettability alteration on dynamic capillary pressure. (external link)

Editorial/Leader article

• Fred Vermolen; Carmen Rodrigo; Francisco José Gaspar et al. (2021). Guest Editorial to the special issue: Computational mathematics aspects of flow and mechanics of porous media: State-of-the-art computational methods in the mechanics and flow in porous media. (external link)
• Florin Adrian Radu; Kundan Kumar; Inga Berre et al. (2019). Preface. (external link)
• Amgad Salama; Shuyu Sun; Mohamed F. El Amin et al. (2017). Flow and transport in porous media: a multiscale focus. (external link)

Book anthology

• Florin Adrian Radu; Kundan Kumar; Inga Berre et al. (2019). Numerical Mathematics and Advanced Applications ENUMATH 2017. (external link)

Research report

• Florin Adrian Radu; Kundan Kumar; Jan Martin Nordbotten et al. (2017). A convergent mass conservative numerical scheme based on mixed finite elements for two-phase flow in porous media. (external link)

Doctoral thesis (PhD)

• David Landa-Marbán; Florin Adrian Radu; Kundan Kumar et al. (2019). Mathematical modeling of microbial enhanced oil recovery with focus on bio-plug technology: from the pore to the core scale. (external link)

Academic literature review

• Amgad Salama; Mohamed F. El Amin; Kundan Kumar et al. (2017). Flow and transport in tight and shale formations: A review. (external link)

See a complete overview of publications in Cristin.

Please see attached CV.

At Google scholar https://scholar.google.com/citations?user=rHFW3EAAAAAJ&hl=en

2016-2017

NFR-DAAD (PI, UoB-University of Erlangen, Germany): Upscaling of Evolving Microstructures and its Applications, (80k NOK).

2015-2016

SIU Project  (PI, UoB-Russian Academy of Sciences, St. Petersburg). An extensive collaborative project on education, research and training with 
Russian Academy of Sciences, St Petersburg, Russia, CPRU 2015/10040, (147k NOK).

2017-2020

NFR-Petromaks2  (Co-applicant, UniResearch CIPR-UoB): EOR upscaling - from lab to field, 2 PhD at UoB); main-adviser for the PhD,  (24M NOK).

2017-2020

NFR-CLIMIT  (Co-applicant, UniResearch CIPR-UoB): Efficient models for Microbially Induced CAlcite Precipitation as a seal for CO2 storage (MICAP), (8M NOK).

2016-2020

NFR-Toppforsk  (Co-applicant): Thermo-Mechanical Subsurface Energy Storage (TheMSeS) (4 PhD, 4 PostDocs); main adviser for 1 PhD, (25M NOK).

2016-2019

NFR-Petromaks2  (Co-applicant, Collaboration UniResearch CIPR-UoB): Improving microbial selective plugging technology through experimentally based modelling and simulation (IMMENS) (1 PhD at UoB); co-adviser for the PhD, (10M NOK).

2016-2019

NFR-CLIMIT  (Co-applicant, UniResearch CIPR-UoB): Fundamentals of CO2- Hydrocarbon Interactions for CO2 storage with enhanced oil recovery (CHI).(7M NOK).

2016-2017

NFR-DAAD  (Co-applicant, UoB-Federal Army University of Hamburg, Germany): Efficient discretizations and fast solvers for poroelasticity, (60k NOK).

2016-2019

UoB/Statoil Project  (Co-author): Experimentally based modelling of colloid transport in multiphase porous media (EPOCH) (1 PostDoc). WP leader, (3.5M NOK).

2020-2022

PI: Strategisk program for internasjonalt forskningssamarbeid, SPIRE UoB, (60k NOK)

 

2021-2026

VISTA Center for Coupled Subsurface Dynamics, UoB, Head of one of three scientific pillars, (25 M NOK)

2023- 2025

Project manager and PI, Modelling and Solution Strategies for the Subsurface Deformations, (200k NOK). Akademiaavtalen.

 

2022-2028

Deputy Head of Work Package 1, Center for Sustainable Subsurface Resources, one of three current petroleum research centers (PETROCENTER), Main supervisor of 1 PhD student.